The complicated electromagnetic couplings between nanostructures present substantial challenges in the design and simulation of metasurfaces, especially large-scale elements. The couplings are typically neglected in a conventional simulation. We introduce a computational framework that includes the electromagnetic coupling effects between meta-atoms. Decomposing the incident field and segmenting the computing range for individual local simulations allows for an effective and accurate simulation of the entire metasurface. Numerical examples of a 2 mm diameter cylindrical metalens with a numerical aperture of 0.9 and a 1 mm aperiodic beam splitter show the deviation from the conventional method is reduced by 97% compared to the rigorous method, while the computation times are 10 times and 4 times faster than the rigorous methods, respectively.

Multilayer coatings are widely used in reflective optical systems, particularly for short-wavelength applications. Such coatings, while playing a key role in enhancing the reflectance, may cause non-negligible aberrations, which are often omitted in the typical optical design and simulation. In this study, we investigate the effects induced by the multilayer coatings and present a practical computational algorithm that correctly considers the lateral shift, the phase change, and the amplitude modulation. Several examples are included to show the effectiveness of the algorithm.

In this paper, a depth-sensing method employing active irradiation of a semi-annular beam is proposed for observing the multi-layered reflective surfaces of transparent samples with higher resolutions and lower interference. To obtain the focusing resolution of the semi-annular aperture diaphragm system, a model for computing the diffracted optical energy distribution of an asymmetric aperture diaphragm is constructed, and mathematical formulas are deduced for determining the system resolution based on the position of the first dark ring of the amplitude distribution. Optical simulations were performed under specific conditions; the lateral resolution ${\delta }_r$ of the depth-sensing system was determined to be 0.68 μm, and the focusing accuracy ${\delta }_z$ was determined to be 0.60 μm. An experimental platform was established under the same conditions, and the results were in accord with those of the simulation results, which validated the correctness of the formula for calculating the amplitude distribution of the diffracted light from the asymmetric aperture diaphragm.

Diffraction significantly deteriorates the quality of the laser image, causing severe degradation that undermines the theoretical performance parameters of the autofocus system. In this paper, we conduct a comprehensive analysis of the non-uniform features of the images. To enhance the imaging quality of each individual image, we propose a de-diffraction algorithm based on gradient iteration. This algorithm is capable of rapidly removing the interference spots resulting from diffraction and restoring the distorted laser spots. By doing so, it effectively eliminates the inevitable reduction in the autofocus resolution and focusing accuracy caused by diffraction. Furthermore, the proposed calculation model for the intra-localisation interval significantly improves the convergence of the iterative calculation process. Through experiments, it has been verified that, under the same conditions, the interlayer resolution between the reflective surfaces of the samples processed using this algorithm is increased to a quarter of the original value. This remarkable improvement in resolution, which far exceeds the microscope’s inherent resolution, demonstrates that the algorithm successfully achieves super-resolution for the microscope.